If a child was born in China by two Chinese parents but was adopted by two American parents, what citizenship does that child have? Does he/she retain the chinese citizenship? Is it possible by adoption to have a duel citizenship of China and United States?
From the little information provided, I would say the child is most likely a US citizen and isn't a Chinese citizen.
If the child was born after 1983, and was in the US as a permanent resident, they would almost certainly have gained US citizenship through the Child Citizenship Act of 2000 (if they hadn't already gained US citizenship before), by being a permanent resident under 18 living in the US with a US-citizen parent.
I believe gaining derivative US citizenship (i.e. US citizenship for minors gained after birth) generally causes loss of Chinese (PRC) nationality. It is a little unclear because the meaning of certain provisions in the Chinese law are not explained in detail. In particular, Article 9 of the PRC Nationality Law provides that if a Chinese citizen voluntarily acquires a foreign nationality, they automatically lose Chinese citizenship. The question is whether derivative US citizenship (which is gained automatically when all the conditions are met, without the child's action or choice) counts as voluntary. Although I cannot cite any authoritative explanation of the Chinese law, I believe it does, because in the case of Chinese-national permanent resident parents and children, where the parent naturalizes, causing the child to automatically derive US citizenship, I think it is pretty widely accepted that the child loses Chinese nationality in this case, and it is the same derivative citizenship process that would apply to the adopted child in this question.
(Note that this is different from the case of children who automatically had US (or other foreign) nationality at birth, and also had Chinese nationality at birth; those children would likely retain dual nationality indefinitely as there is no provision for them to lose Chinese nationality. Article 9 doesn't apply as nationality at birth is obviously involuntary, and in any case foreign nationality at birth occurs simultaneously with Chinese nationality at birth so it wouldn't make sense to have loss of nationality anyway.)